Machining apparatuses for machining metal workpieces by removing material, e.g. burnishing machines, grinding machines or deburring machines, are known. In this case, use is made, for example, of circulating machining materials, such as friction belts or grinding belts, which run past regions of the workpiece that are to be machined, a working side of the belt being moved in the direction of the workpiece. In order to be able to influence the machining action, in particular during preparation for removing protruding or rough material regions even of highly profiled workpieces, various pressure mechanisms have hitherto been realized for machining belts, but these pressure mechanisms are not yet entirely satisfactory.